Abstract
This paper presents a method for calibrating a multicurrency lognormal LIBOR Market Model (MC-LMM) to market data of at–the–money caps, swaptions and FX options. By exploiting the fact that multivariate normal distributions are invariant under orthonormal transformations, the calibration problem is decomposed into manageable stages, calibrating to market-observed implied volatilities and the no-arbitrage conditions linking forward exchange rates and the term structure of interest rates in each currency, while maintaining the ability to achieve realistic correlation structures between all modelled market variables. The key to achieving a fast and efficient calibration lies in the method to estimate the orthonormal transformations. Firstly, we recall a method of least-squares estimation of an orthonormal transformation known as orthonormal procrustes, which goes back to Schonemann (1966). Secondly, we demonstrate how to use the method in MC-LMM calibration.
Joint work with Kay F. Pilz
[PDF] Slides of the presentation.